Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$

Details Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$ Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$

1995-09-22

arxiv.org/abs/math/9509214v1

Mathematics

Functional Analysis

Scientific paper

We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements.

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